Unraveling the mathematical euphoria of N = 2³+3³+4³+5³+6³+7³+8³+9³

Continue reading “Joyful Cubes!”## Unlocking the Fraction

Use a trick to quickly and effortlessly determine the fraction that falls between 3/4 and 4/5.

## Math & Art

In 1895, Nicholas Bogdanov-Belsky created the iconic painting “Mental Arithmetic in the Public School of S. Rachinsky,” now a classic. Students are depicted trying to solve the problem on the blackboard: (10²+11²+12²+13²+14²)/365. They seem to be having a great time!

## A Curious Constant

A palindromic number is an integer that remains the same when its digits are reversed. The sum of the reciprocals of all the palindromic numbers in the world converges to approximately *3.3703… *

## Summation Formulas

Some remarkable summation formulas…

## φibonacci formula

Because F* _{n}*→ φ

*ⁿ*when

*n*→ ∞

## When matrices meet Fibonacci

F_{0} = 1, F_{1} = 1, F* _{n}* = 1, F

*= F*

_{n}

_{n}_{-1}+ F

_{n}_{-2},

*n*≥ 2

Read more: https://mathworld.wolfram.com/FibonacciQ-Matrix.html

## Perfect “Square” Circle

Numbers 1 to 32 are placed along the circumference of a circle without repeating any number and still the sum of any two adjacent numbers in this circle is a perfect square!

## Sum of Consecutive Cubes (Visual Proof)

The sum of the first *n* cubes is the square of the *n*th triangular number:

1^{3} + 2^{3} + 3^{3} + 4^{3} + 5^{3} + . . . + *n*^{3} = (1 + 2 + 3 + 4 + 5 + . . . + *n*)^{2}.

## Inverse Powers of Phi

Summation of Alternating Inverse Powers of Phi…